Advances in Difference Equations
Volume 2009 (2009), Article ID 973709, 14 pages
doi:10.1155/2009/973709
A functional inequality in restricted domains of Banach modules
M.B. Moghimi1
, Abbas Najati1
and Choonkil Park3
1Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran
3Department of Mathematics, Hanyang University, Seoul 133-791, South Korea
Abstract
We investigate the stability problem for the following functional inequality ∥αf((x+y)/2α)+βf((y+z)/2β)+γf((z+x)/2γ)∥≤∥f(x+y+z)∥ on restricted domains of Banach modules over a C∗-algebra. As an application we study the asymptotic behavior of a generalized additive mapping.